Independent TDs have expressed frustration at the breakdown in talks between the main parties.

Shane Ross of the Independent Alliance (IA), said: "It's very disappointing that after refusing to talk for 42 days the two big parties could only hold two meetings, one for a hour and one for a mere 10 minutes. They should get back into discussions about forming a minority government immediately."

Denis Naughten of the 'Rural Five' group of Independents said he had been hoping Mr Martin wouldn't "reject this olive branch from Enda Kenny" and encouraged Fianna Fáil "not to dismiss any suggestions that are being put forward".

"We felt that this (partnership government) was a sensible way forward and that's why we suggested it because we felt it was a way to resolve this impasse," he said.

He warned that a minority government would be "very challenging" due to the constraints on this year's Budget as outlined by Finance Minister Michael Noonan last week.

Another 'Rural Five' member, Tipperary's Mattie McGrath, said: "I'm not wasting any more time on talks. It's up to Fine Gael and Fianna Fáil to come back to us with a roadmap now."

IA deputy Seán Canney said he wasn't surprised that Fianna Fáil rejected Mr Kenny's first offer, but said: "Enda Kenny and Micheál Martin need to have another sit down... and see can they pull something together."

Dublin Central TD Maureen O'Sullivan said both parties should "accept the reality of the vote" and "get on with it".

"There's too many serious issues we're waiting on and there's no point having more Dáil statements on housing. We're looking for action and that's not going to happen until we get a government," she said.